According to a survey of American households, the probability that the residents own two cars if annual household income is over $50,000 is 80%. Of the households surveyed, 60% had incomes over $50,000 and 70% had two cars. The probability that the residents of a household own two cars and have an income over $50,000 a year is ________.
A) 0.12
B) 0.18
C) 0.22
D) 0.48

Question

Quizplus · Accepted Answer

Using Bayes' theorem, we can find the probability:

P(income > $50k and 2 cars) = P(2 cars | income > $50k) * P(income > $50k) 
= 0.8 * 0.6 
= 0.48

Therefore, the answer is D.

According to a Survey of American Households, the Probability That